428 THE ELECTROMAGNETIC FIELD. [PT. III. CH. XI. 



In like manner 



1 2 x 2 



a 



* 2 * 2 



cos (ry) cos (ds^ds^) - cos (ds. 2 y) cos 



cos rs cos ss^) cos cg-z cos 



The resultant (ZlR has a component 



/j/aCfeiCfoa COS 



in the direction of r, and one of magnitude 



cos (r, 



in the direction ds 2 . This resolution into infinitesimal forces is 

 unfortunate on account of the lack of symmetry with regard to 

 the two elements. 



220. Mutual Energy of two Currents. The whole force 

 acting on the circuit 1 is found by integrating the expressions (7) 

 already found for c 2 E, c 2 H, d 2 Z, around both circuits 1 and 2, 



.. 



(8) %= IJ Z \ -r^- [dx l dx 2 + dy l dy z + dz 



J iJ 2 3\ 



with similar expressions for H and Z. If we now suppose the 

 circuit 1 displaced or deformed in any manner, so that a point 

 #1, 2/i > z \> i g displaced by the amount &EJ, Sy lf 8&i the circuit 2 

 being fixed, the forces H, H, Z do the work 



(9) 



dydy<i -\- dz^dz^ 



> , . 



- | I 



JiJa 



